SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #3 : Creating Equations With Whole Numbers

What is the solution of  that satisfies both equations?

Possible Answers:

Correct answer:

Explanation:

Reduce the second system by dividing by 3.

Second Equation:

     We this by 3.

Then we subtract the first equation from our new equation.

First Equation:

First Equation - Second Equation:

Left Hand Side:

Right Hand Side:

Our result is:

Example Question #43 : Systems Of Equations

What is the solution of  for the two systems of equations?

Possible Answers:

Correct answer:

Explanation:

We first add both systems of equations.

Left Hand Side:

Right Hand Side:

Our resulting equation is:

 

We divide both sides by 3.

Left Hand Side:

Right Hand Side:

Our resulting equation is:

Example Question #4 : Creating Equations With Whole Numbers

What is the solution of  for the two systems?

Possible Answers:

Correct answer:

Explanation:

We first multiply the second equation by 4.

So our resulting equation is:

Then we subtract the first equation from the second new equation.

Left Hand Side:

Right Hand Side:

Resulting Equation:

 

We divide both sides by -15

Left Hand Side:

Right Hand Side:

Our result is:

 

Example Question #51 : Systems Of Equations

The cost of buying 1 shirt and 2 pants is $110 and cost of buying 4 shirts and 3 pants is $200. Assume that all shirts have the same cost and all pants have the same cost. What is the cost of one shirt and one pair of pants in dollars? 

Possible Answers:

Correct answer:

Explanation:

Let s equal the cost of the shirt and p equal to the cost of a pair of pants. The question can be set up as follows:

The top equation can be multiplied by 4 to give:

The bottom equation can be subtracted from the top equation to give:

Dividing by 5 gives the cost of a pair of pants:

This can be plugged into either one of the initial equations to solve for the cost of the shirt.

Subtracting both sides by 96 gives:

The question asks for the cost of a pair of pants and a shirt which is the sume of the costs. 

Example Question #268 : Algebra

Solve for the point of intersection of the following two lines:  

Possible Answers:

Correct answer:

Explanation:

Solve for  or  first.  Let's solve for .  To do this, we must eliminate the  variables.  Multiply the first equation by the coefficient of the  variable in the second equation.

Subtract the second equation from the first equation and solve for .

Resubstitute this value to either original equations.  Let's substitute this value into .

Find the common denominator and solve for the unknown variable.

The correct answer is:  

Example Question #51 : Systems Of Equations

If  and , what is the value of ?

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

If  then adding  is equal to . If  then  or .  This means that  is equal to  or .

Example Question #271 : Algebra

Solve the following system of equations:

 

Possible Answers:

Correct answer:

Explanation:

We can solve this system of equations by elimination. 

By adding the second equation to the first, we get  or .

Substitute y=-4 into either equation and solve for x. 

Simplify and solve for x to get .

Therefore, the solution to this system of equations as an ordered pair is (7, -4). 

Example Question #53 : Systems Of Equations

You've gone to a bakery to get some fresh baked goods. You notice that the person in front of you in the checkout line buys 3 scones and 4 donuts for $10. You get 3 scones and 5 donuts for $12. How much do donuts cost at the bakery?

Possible Answers:

Correct answer:

Explanation:

We can express this problem as a system of equations where s represents scones and d represents donuts. 

We can solve this system of equations by elimination as follows:

Subtracting the second equation from the first yields  or 

Therefore, donuts cost $2. 

Example Question #51 : How To Find The Solution For A System Of Equations

Louise and Jon are running for Student Body President. At their school, a total of 250 students vote in the election. Louise receives 50 more votes than Jon. If everyone votes only once, what percentage of the vote did Louise receive?

Possible Answers:

Correct answer:

Explanation:

We can express the given information as a system of equations. Let L represent the votes cast for Lisa, and let J represent the votes cast for Jon. 

The total votes cast in the election can be written as

Since Lisa received 50 more votes than Jon, we can write

We can solve this system of equations by substitution.

Let's rewrite the second equation in terms of J. 

.

 

Now, we can substitute  into .

This gives us

 

We can simplify this to get .

 

To calculate the percentage of the votes that were cast for Lisa, we take her 150 votes and divide them by the total number of votes cast in the election. Then, we multiply that by 100%.

0.6 x 100% = 60%

Example Question #272 : Algebra

The sum of four consecutive even integers is , but their product is . What is the least of those integers?

Possible Answers:

Correct answer:

Explanation:

Any time the product of consecutive numbers is , must be a one of those consecutive numbers, because if it is not, the product will be non-zero. This leaves us with four possibilities, depending on where  is placed in the sequence.

As we can see, , , and are our numbers in question, meaning is our answer as the lowest number.

Note that it is possible to use algebra and set up a system of equations, but it's more time-consuming, which could hinder more than help in a standardized test setting.

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